A Novel Affine Arithmetic Method to Solve Optimal Power Flow Problems With Uncertainties

Load Flow Analysis of a Power System Network in the Presence of Uncertainty using Complex Affine Arithmetic

“…The outcome confirms the conservative nature of AA over MC approach. This is mainly due to Monte Carlo approach does not consider round-off and truncation errors better than AA [10], [13], [14]. The AA based power flow analysis has been done by researchers so far is based on sensitivity analysis which adds an extra burden to the computation.…”

“…The AA based power flow analysis has been done by researchers so far is based on sensitivity analysis which adds an extra burden to the computation. Besides, the Newton-Raphson method needs high orders of Chebyshev approximation in order to represent the trigonometric functions [10], [13], [14], [19]. A GaussSeidel algorithm is used in this paper to solve the growth of non-affine operations, which does not need sensitivity analysis to start the simulation and free from higher order Chebyshev approximation.…”

“…IA takes into consideration the uncertainties in the system and gives strict bound [11]. But, AA on the other hand gives a conservative bound because of its consideration of round-off and truncation error, besides input uncertainty, better than IA [13], [14]. Both IA and AA based analysis are validated by comparing the result with probabilistic Monte Carlo approach.…”

An efficient two stage stochastic optimal energy and reserve management in a microgrid

“…It provided less conservative bounds without demanding for probability distribution functions. Hence, modern OPF methods [24][25][26] use these alternative approaches for stochastic estimation of state and control variable intervals. These methods solely considered a maximum uncertainty without commenting on the lower levels of uncertainties.…”

Robust voltage regulation in unbalanced radial distribution system under uncertainty of distributed generation and loads

“…Uncertainties can be considered using fuzzy logic [9,10], stochastic approaches [11][12][13][14][15][16], interval arithmetic [17,18], reachability set [19] or robust optimization technique [20]. Both fuzzy logic and stochastic approaches provide no guarantee that a solution will be always feasible for all possible combinations of generations and loads.…”